tg60cos15-sin15=tg60cos(45-30)-sin(45-30)=
tg60(1/2)(cos45cos30+sin45sin30)-(1/2)(sin45cos30-cos45sin30)=
sqrt3*(1/2)(sqrt2/2*1/2+sqrt2/2*1/2)-1/2*(sqrt2/2*sqrt3/2-sqrt2/2*1/2)=
sqrt3 sqrt2 1 sqrt6-sqrt2 sqrt6 sqrt6-sqrt2 sqrt6+sqrt2
------*------- - ----* (----------------)=--------- - -------------- = -------------
2 2 2 4 4 8 8